For instance, we know how to translate the hieroglyphics because of the Rosetta Stone. I'm aware that Old English is far more similar to known languages than the hieroglyphics, but looking at the original text of Beowulf I still don't see a single word I can make sense of. How did they learn to translate Old English accurately?
Loads of Anglo-Saxon documents survive, such as The Anglo-Saxon Chronicle. Coupled with the fact that Old English is a West Germanic language sharing many cognates with other languages in Europe, translation is fairly easy and affords one the luxury of speculating about the pronunciation as well. One can also look to irregularities in modern English for clues as to how Old English was structured, as seen for example in the irregular plural form of loaf --> loaves.
With regards to reading Beowulf, knowing a modern Germanic language would help you greatly, such as Dutch. Alternatively, try reading the text out loud.